A simple model for the estimation of the maximum percentage of deaths due to COVID-19.
NOTE: I’m not an epidiomiologist.
The prediction based on a simple logistic model and:
70% of SARS-CoV-2 exposure
10% Infection efficacy ie. 10% of the exposure subjects turns into a Covid-19 case
1% of Mortality
For each country we will use the urban population
I’ll estimate the death rates based on current trends fitted to the logistic function.
The last 14 days will be used for the peak estimations. Peak estimations will be done using:
# The expetec % of deaths in each country
expectedtotalFatalities = 0.7*0.1*0.01
# The number of observations used for the trends
daysWindow <- 14
currentdate <- "April 7:"
The data is the training set from: Kaggle: COVID19 Global Forecasting (Week 3)
https://www.kaggle.com/c/covid19-global-forecasting-week-3/data
train <- read.csv("~/GitHub/COVIDTrends/Kaggle/train.csv", stringsAsFactors=FALSE)
train$ProviceCountry <- paste(train$Country_Region,train$Province_State,sep=":")
train[train$Country_Region=="Korea, South","Country_Region"] <- "South Korea"
trainCountry <- train[train$Province_State == "",]
covid19_datapopulation <- read.csv("~/GitHub/COVIDTrends/Kaggle/covid19_data - population.csv", stringsAsFactors=FALSE)
rownames(covid19_datapopulation) <- paste(covid19_datapopulation$Country,":",sep="")
totalPoulation <- as.numeric(str_replace_all(covid19_datapopulation$Population_2020,",",""))
totalUrbanPoulation <- as.numeric(str_replace_all(covid19_datapopulation$Urban_pop_pct,"\\%",""))/100.0
totalUrbanPoulation[is.na(totalUrbanPoulation)] <- 1.0;
totalUrbanPoulation <- totalPoulation*totalUrbanPoulation
covid19_datapopulation$ExpectedFatalities <- expectedtotalFatalities*(
totalUrbanPoulation +
0.1*(totalPoulation-totalUrbanPoulation)
)
trainCountry$PerFatalities <- trainCountry$Fatalities/covid19_datapopulation[trainCountry$Country_Region,"ExpectedFatalities"]
trainCountry <- trainCountry[trainCountry$Fatalities > 0,]
expfatalities <- covid19_datapopulation$ExpectedFatalities/1.0e6
names(expfatalities) <- covid19_datapopulation$Country
expfatalities <- expfatalities[order(-expfatalities)]
plot.new()
op <- par(no.readonly = TRUE)
par(mar=c(8,4,4,4),pty="m")
#barplot(expfatalities[1:30],las=2,cex.names =0.70,cex.axis = 0.60,horiz = TRUE,main="Expected Fatalities",xlab="MIllions")
barplot(expfatalities[1:30],las=2,cex.names =0.70,cex.axis = 0.60,main="Expected Fatalities",ylab="Millions")
par(op)
Ploting some trends
Country_Region <- names(table(trainCountry$Country_Region))
totaldeaths <- numeric()
for (ctr in Country_Region)
{
totaldeaths <- append(totaldeaths,max(trainCountry[trainCountry$Country_Region == ctr,"Fatalities"]))
}
names(totaldeaths) <- Country_Region
totaldeaths <- totaldeaths[order(-totaldeaths)]
plot(trainCountry[trainCountry$Country_Region == names(totaldeaths[1]),"Fatalities"],main="Fatalities",xlab="Days",ylab="Fatalities")
for (ctr in names(totaldeaths[1:25]))
{
linp <- trainCountry[trainCountry$Country_Region == ctr,"Fatalities"]
lines(linp)
text(length(linp)-1,linp[length(linp)],ctr)
}
plot(trainCountry[trainCountry$Country_Region == names(totaldeaths[1]),"PerFatalities"],main="% Fatalities",xlab="Days",ylab=" % Fatalities")
for (ctr in names(totaldeaths[1:25]))
{
linp <- trainCountry[trainCountry$Country_Region == ctr,"PerFatalities"]
lines(linp)
text(length(linp)-1,linp[length(linp)],ctr)
}
totaldeaths <- totaldeaths[totaldeaths > 100]
par(op)
cn = 20
par(mfrow=c(1,1),cex=0.65,mar=c(4,4,4,5))
for (cn in c(1:length(totaldeaths)))
{
endDay <- 0
countryNumber <- cn
mainName <- paste(currentdate,names(totaldeaths[countryNumber]))
datsetone <- trainCountry[trainCountry$Country_Region == names(totaldeaths[countryNumber]),"PerFatalities"]
datsetchange <- c(datsetone[1],datsetone[2:length(datsetone)]-datsetone[1:(length(datsetone)-1)])
lastobs <- length(datsetone)
datsetchange <- 0.35*datsetchange +
0.65*c(datsetone[1],0.5*(datsetone[3:lastobs]-datsetone[1:(length(datsetone)-2)]),datsetchange[lastobs])
datasetone <- as.data.frame(cbind(days=c(1:length(datsetone)),fatalities = datsetone,newfatalities = datsetchange))
numdays <- nrow(datasetone)
ndays <- max(c(numdays - endDay,7))
startday <- max(1,ndays - daysWindow)
daysrange <- c(startday:ndays)
roestimate <- try(nls(fatalities ~ logisticcdf(days, ro, to),
data = datasetone[daysrange,],
start=list(ro= -0.1,to=ndays),
control=list(warnOnly=TRUE)))
if (!inherits(roestimate, "try-error"))
{
smo <- summary(roestimate)
predictedTotalCases <- logisticcdf(c(1:120),smo$coefficients[1,1],smo$coefficients[2,1])
ymax <- max(c(predictedTotalCases,datasetone$fatalities))
plot(predictedTotalCases,ylim=c(0,1.0),type="l",lty=2,xlab="days",ylab="Fraction of the Total Expected Fatalities",main=mainName)
lines(datasetone$days[c(1:ndays)],datasetone$fatalities[c(1:ndays)],lwd=5)
lines(datasetone$days[c(1:ndays)],10*datasetone$newfatalities[c(1:ndays)],lty=3,lwd=4,col=2)
daycode <- c("Last:","One Week Ago:","Two Weeks Ago:","Three Weeks Ago:")
dc <- 1
for (endDay in c(0,7,14,21,28))
{
ndays <- numdays - endDay
if (ndays > 7)
{
startday <- max(1,ndays - daysWindow)
daysrange <- c(startday:ndays)
pdfestimate <- try(nls(newfatalities ~ logisticpdf(days, ro, to),
data = datasetone[daysrange,],
start=list(ro= smo$coefficients[1,1],to=smo$coefficients[2,1]),
control=list(warnOnly=TRUE)))
if (!inherits(pdfestimate, "try-error"))
{
nsmo <- summary(pdfestimate)
newcases <- logisticpdf(c(1:120),nsmo$coefficients[1,1],nsmo$coefficients[2,1])
lines(10*newcases,lty=6,col=(endDay+7)/7,lwd= 1 + 1*(dc == 1))
dmax <- which.max(newcases)
daystopeak <- nsmo$coefficients[2,1]-numdays;
if (dc == 1)
{
text(dmax+7,10*max(newcases)+0.05,paste("Days to Peak:",sprintf("%3.0f",daystopeak)),cex=0.8)
}
}
}
dc <- dc + 1
}
}
else
{
plot(datasetone$days[c(1:ndays)],datasetone$fatalities[c(1:ndays)],
ylim=c(0,1.0),
type="l",
lty=2,
xlab="days",
ylab="% Fatalities",
main=mainName)
}
legend("topright",
legend = c("Estimated","Observed","New Fatalities","Estimated New","One Week Ago","Two Weeks Ago","Three Weeks Ago","Four Weeks Ago"),
col = c(1,1,2,1,2,3,4,5),
lty = c(2,1,3,6,6,6,6,6),
lwd = c(1,5,4,2,1,1,1,1))
z <- c(0:10)/100;
axis(4, at=10*z,labels=round(z,digits=2),
col.axis="blue", las=2, cex.axis=0.7, tck=-.01)
mtext("Fraction of New Fatalities", cex=0.5,side=4, line=3, cex.lab=0.3, col="black",las=3)
}
trainProvince <- train[train$Province_State != "",]
#locations_population <- read.csv("~/GitHub/COVIDTrends/Kaggle/locations_population.csv", stringsAsFactors=FALSE)
library(readxl)
locations_population <- read_excel("Kaggle/locations_population.xlsx")
totalStatePoulation <- as.numeric(locations_population$UrabPop)
names(totalStatePoulation) <- locations_population$Province.State
totalStatePoulation <- totalStatePoulation[locations_population$Province.State != ""]
trainProvince$PerFatalities <- (trainProvince$Fatalities/totalStatePoulation[trainProvince$Province_State])/expectedtotalFatalities
trainProvince <- trainProvince[trainProvince$Fatalities > 0,]
Province_State <- names(table(trainProvince$Province_State))
totaldeaths <- numeric()
for (ctr in Province_State)
{
totaldeaths <- append(totaldeaths,max(trainProvince[trainProvince$Province_State == ctr,"Fatalities"]))
}
names(totaldeaths) <- Province_State
totaldeaths <- totaldeaths[order(-totaldeaths)]
totaldeaths <- totaldeaths[totaldeaths>100]
par(op)
cn = 2
par(mfrow=c(1,1),cex=0.65,mar=c(4,4,4,5))
for (cn in c(1:length(totaldeaths)))
{
endDay <- 0
stateNumber <- cn
mainName <- paste(currentdate,names(totaldeaths[stateNumber]))
datsetone <- trainProvince[trainProvince$Province_State == names(totaldeaths[stateNumber]),"PerFatalities"]
datsetchange <- c(datsetone[1],datsetone[2:length(datsetone)]-datsetone[1:(length(datsetone)-1)])
lastobs <- length(datsetone)
datsetchange <- 0.35*datsetchange +
0.65*c(datsetone[1],0.5*(datsetone[3:lastobs]-datsetone[1:(length(datsetone)-2)]),datsetchange[lastobs])
datasetone <- as.data.frame(cbind(days=c(1:length(datsetone)),fatalities = datsetone,newfatalities = datsetchange))
numdays <- min(nrow(datasetone),which.max(datasetone$newfatalities)+7)
ndays <- max(c(numdays - endDay,7))
startday <- max(1,ndays - daysWindow)
daysrange <- c(startday:ndays)
roestimate <- try(nls(fatalities ~ logisticcdf(days, ro, to),
data = datasetone[daysrange,],
start=list(ro= -0.1,to=ndays),
control=list(warnOnly=TRUE)))
if (!inherits(roestimate, "try-error"))
{
smo <- summary(roestimate)
predictedTotalCases <- logisticcdf(c(1:120),smo$coefficients[1,1],smo$coefficients[2,1])
ymax <- max(c(predictedTotalCases,datasetone$fatalities))
plot(predictedTotalCases,ylim=c(0,1.0),type="l",lty=2,xlab="days",ylab="Fraction of the Total Expected Fatalities",main=mainName)
lines(datasetone$days[c(1:ndays)],datasetone$fatalities[c(1:ndays)],lwd=5)
lines(datasetone$days[c(1:ndays)],10*datasetone$newfatalities[c(1:ndays)],lty=3,lwd=4,col=2)
daycode <- c("Last:","One Week Ago:","Two Weeks Ago:","Three Weeks Ago:")
dc <- 1
endDay <- 0;
for (endDay in c(0,7,14,21,28))
{
ndays <- numdays - endDay
if (ndays > 7)
{
startday <- max(1,ndays - daysWindow)
daysrange <- c(startday:ndays)
pdfestimate <- try(nls(newfatalities ~ logisticpdf(days, ro, to),
data = datasetone[daysrange,],
start=list(ro= smo$coefficients[1,1],to=smo$coefficients[2,1]),
control=list(warnOnly=TRUE)))
if (!inherits(pdfestimate, "try-error"))
{
nsmo <- summary(pdfestimate)
newcases <- logisticpdf(c(1:120),nsmo$coefficients[1,1],nsmo$coefficients[2,1])
lines(10*newcases,lty=6,col=(endDay+7)/7,lwd= 1 + 1*(dc == 1))
dmax <- which.max(newcases)
daystopeak <- nsmo$coefficients[2,1]-numdays;
if (dc == 1)
{
text(dmax+7,10*max(newcases)+0.05,paste("Days to Peak:",sprintf("%3.0f",daystopeak)),cex=0.8)
}
}
}
dc <- dc + 1
}
}
else
{
plot(datasetone$days[c(1:ndays)],datasetone$fatalities[c(1:ndays)],
ylim=c(0,1.0),
type="l",
lty=2,
xlab="days",
ylab="% Fatalities",
main=mainName)
}
legend("topright",
legend = c("Estimated","Observed","New Fatalities","Estimated New","One Week Ago","Two Weeks Ago","Three Weeks Ago","Four Weeks Ago"),
col = c(1,1,2,1,2,3,4,5),
lty = c(2,1,3,6,6,6,6,6),
lwd = c(1,5,4,2,1,1,1,1))
z <- c(0:10)/100;
axis(4, at=10*z,labels=round(z,digits=2),
col.axis="blue", las=2, cex.axis=0.7, tck=-.01)
mtext("Fraction of New Fatalities", cex=0.5,side=4, line=3, cex.lab=0.3, col="black",las=3)
}